A matheuristic for the Distance-Constrained Close-Enough Arc Routing Problem

[EN] The Close-Enough Arc Routing Problem, also called Generalized Directed Rural Postman Problem, is an arc routing problem with interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets within a certain distance of a meter, the receiver is able to record the gas, water, or electricity consumption. Therefore, the vehicle does not need to traverse every street, but only a few, in order to be close enough to each meter. In this paper we deal with an extension of this problem, the Distance-Constrained Generalized Directed Rural Postman Problem or Distance-Constrained Close Enough Arc Routing Problem, in which a fleet of vehicles is available. The vehicles have to leave from and return to a common vertex, the depot, and the length of their routes must not exceed a maximum distance (or time). For solving this problem we propose a matheuristic that incorporates an effective exact procedure to optimize the routes obtained. Extensive computational experiments have been performed on a set of benchmark instances and the results are compared with those obtained with an exact procedure proposed in the literature.This work was supported by the Spanish Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional (FEDER) through Project MTM2015-68097-P (MINECO/FEDER). Authors want to thank two anonymous referees for their suggestions and comments that have contributed to improve the paper.Corberán, A.; Plana, I.; Reula, M.; Sanchís Llopis, JM. (2019). A matheuristic for the Distance-Constrained Close-Enough Arc Routing Problem. Top. 27(2):312-326. https://doi.org/10.1007/s11750-019-00507-3S312326272Aráoz J, Fernández E, Franquesa C (2017) The generalized arc routing problem. TOP 25:497–525Ávila T, Corberán Á, Plana I, Sanchis JM (2016) A new branch-and-cut algorithm for the generalized directed rural postman problem. Transportation Science 50:750–761Ávila T, Corberán Á, Plana I, Sanchis JM (2017) Formulations and exact algorithms for the distance-constrained generalized directed rural postman problem. EURO Journal on Computational Optimization 5:339–365Cerrone C, Cerulli R, Golden B, Pentangelo R (2017) A flow formulation for the close-enough arc routing problem. In Sforza A. and Sterle C., editors, Optimization and Decision Science: Methodologies and Applications. ODS 2017., volume 217 of Springer Proceedings in Mathematics & Statistics, pages 539–546Corberán Á, Laporte G (editors) (2014) Arc Routing: Problems,Methods, and Applications. MOS-SIAM Series on Optimization,PhiladelphiaCorberán Á, Plana I, Sanchis J.M (2007) Arc routing problems: data instances. http://www.uv.es/~corberan/instancias.htmDrexl M (2007) On some generalized routing problems. PhD thesis, Rheinisch-Westfälische Technische Hochschule, Aachen UniversityDrexl M (2014) On the generalized directed rural postman problem. Journal of the Operational Research Society 65:1143–1154Gendreau M, Laporte G, Semet F (1997) The covering tour problem. Operations Research 45:568–576Hà M-H, Bostel N, Langevin A, Rousseau L-M (2014) Solving the close enough arc routing problem. Networks 63:107–118Mourão MC, Pinto LS (2017) An updated annotated bibliography on arc routing problems. Networks 70:144–194Renaud A, Absi N, Feillet D (2017) The stochastic close-enough arc routing problem. Networks 69:205–221Shuttleworth R, Golden BL, Smith S, Wasil EA (2008) Advances in meter reading: Heuristic solution of the close enough traveling salesman problem over a street network. In: Golden BL, Raghavan S, Wasil EA (eds) The Vehicle Routing Problem: Lastest Advances and New Challenges. Springer, pp 487–50

A New Branch-and-Cut Algorithm for the Generalized Directed Rural Postman Problem

The generalized directed rural postman problem, also known as the close-enough arc routing problem, is an arc routing problem with some interesting real-life applications, such as routing for meter reading. In this article we introduce two new formulations for this problem as well as various families of new valid inequalities that are used to design and implement a branch-and-cut algorithm. The computational results obtained on test bed instances from the literature show that this algorithm outperforms the existing exact methodsThe authors wish to thank Minh Hoang Ha, Nathalie Bostel, Andre Langevin, and Louis-Martin Rousseau for providing their instances. The authors also thank the Spanish Ministerio de Economia y Competitividad [project MTM2012-36163-C06-02] and the Generalitat Valenciana [project GVPROMETEO2013-049] for their support.Ávila, T.; Corberán, Á.; Plana, I.; Sanchís Llopis, JM. (2016). A New Branch-and-Cut Algorithm for the Generalized Directed Rural Postman Problem. Transportation Science. 50(2):750-761. https://doi.org/10.1287/trsc.2015.0588S75076150

Concerning a Decision-Diagram-Based Solution to the Generalized Directed Rural Postman Problem

Decision-diagram-based solutions for discrete optimization have been persistently studied. Among these is the use of the zero-suppressed binary decision diagram, a compact graph-based representation for a specified family of sets. Such a diagram may work out combinatorial problems by efficient enumeration. In brief, an extension to the frontierbased search approach for zero-suppressed binary decision diagram construction is proposed. The modification allows for the inclusion of a class-determined constraint in formulation. Variations of the generalized directed rural postman problem, proven to be nondeterministic polynomial-time hard, are solved on some rapid transit systems as illustration. Lastly, results are juxtaposed against standard integer programming in establishing the relative superiority of the new technique

A two-stage solution approach for the Directed Rural Postman Problem with Turn Penalties

In this paper, we consider the Directed Rural Postman Problem with Turn Penalties (DRPP-TP). A solution is a tour that traverses all required arcs of the graph. The total cost of the tour is the sum of the lengths of the traversed arcs plus the penalties associated with the turns. One solution approach involves transforming the arc routing problem into an equivalent node routing problem. An alternative direct approach (without graph transformation) that involves two stages has been proposed in the literature. In the first part of this paper, we investigate the applicability of the direct approach. We identify several characteristics of the input instance that make this approach effective and present several limitations of this approach. In the second part of this paper, we describe an integer linear program that is combined with a local search algorithm. This combination produces high-quality solutions to the DRPP-TP in a reasonable amount of computing time. (C) 2018 Published by Elsevier B.V

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577

The generalized arc routing problem

The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-017-0437-4This paper focuses on the generalized arc routing problem. This problem is stated on an undirected graph in which some clusters are defined as pairwise-disjoint connected subgraphs, and a route is sought that traverses at least one edge of each cluster. Broadly speaking, the generalized arc routing problem is the arc routing counterpart of the generalized traveling salesman problem, where the set of vertices of a given graph is partitioned into clusters and a route is sought that visits at least one vertex of each cluster. A mathematical programming formulation that exploits the structure of the problem and uses only binary variables is proposed. Facets and families of valid inequalities are presented for the polyhedron associated with the formulation and the corresponding separation problem studied. The numerical results of a series of computational experiments with an exact branch and cut algorithm are presented and analyzed.Peer ReviewedPostprint (author's final draft

Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

Testing a distributed system: Generating minimal synchronised test sequences that detect output-shifting faults

A distributed system may have a number of separate interfaces called ports and in testing it may be necessary to have a separate tester at each port. This introduces a number of issues, including the necessity to use synchronised test sequences and the possibility that output-shifting faults go undetected. This paper considers the problem of generating a minimal synchronised test sequence that detects output-shifting faults when the system is specified using a finite state machine with multiple ports. The set of synchronised test sequences that detect output-shifting faults is represented by a directed graph G and test generation involves finding appropriate tours of G. This approach is illustrated using the test criterion that the test sequence contains a test segment for each transition

An updated annotated bibliography on arc routing problems

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio